Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

Page concordance

< >
Scan Original
281 269
282 270
283 271
284 272
285 273
286 274
287 275
288 276
289 277
290 278
291 279
292 280
293 281
294 288
295 283
296 284
297 285
298 286
299 287
300 288
301 289
302 290
303 291
304 292
305 293
306 294
307 295
308 296
309 297
310 298
< >
page |< < (265) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div518" type="section" level="3" n="8">
              <div xml:id="echoid-div521" type="letter" level="4" n="2">
                <pb o="265" rhead="EPISTOLAE." n="277" file="0277" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0277"/>
              </div>
              <div xml:id="echoid-div524" type="letter" level="4" n="3">
                <head xml:id="echoid-head396" style="it" xml:space="preserve">De inuentione axis propoſite portionis datæ ſphæræ.</head>
                <head xml:id="echoid-head397" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3308" xml:space="preserve">VTaxem propoſitæ alicuius datæ ſphæræ inuenire poſſis ita tibi operandum eſt
                    <lb/>
                  vt gratia exempli. </s>
                  <s xml:id="echoid-s3309" xml:space="preserve">Propoſita nobis eſt ſphæra
                    <var>.c.i.e.t.</var>
                  diametri cognitæ. </s>
                  <s xml:id="echoid-s3310" xml:space="preserve">pro
                    <lb/>
                  poſita etiam eſt nobis eius portio
                    <var>.n.e.u.</var>
                  axis
                    <var>.e.a.</var>
                  cognitæ minoris ſemidiametro, da-
                    <lb/>
                  ta etiam nobis eſt proportio alterius portionis minoris hemiſphærio
                    <var>.i.e.t.</var>
                  ad por-
                    <lb/>
                  tionem
                    <var>.n.e.u.</var>
                  quæritur nunc quantus ſit axis
                    <var>.e.x.</var>
                  ſecundæ portionis hoc eſt deſidera-
                    <lb/>
                  mus cognoſcere proportionem
                    <var>.e.x.</var>
                  ad
                    <var>.e.a.</var>
                  vel ad diametrum ipſius ſpheræ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3311" xml:space="preserve">Cuius gratia reperiatur primò proportio
                    <reg norm="circunferentiæ" type="context">circũferentiæ</reg>
                  maioris circuli ipſius
                    <reg norm="ſphae­ ræ" type="simple">ſphę­
                      <lb/>
                    ræ</reg>
                  adeius diametrum, quæ ferè eſt vt .22. ad .7. ex Archimede.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3312" xml:space="preserve">Quo facto, inueniatur quantitas ſuperficialis huiuſmodi maioris circuli, quæ ſem-
                    <lb/>
                  per æqualis eſt producto quod fit ex ſemidiametro in dimidium circunferentiæ ip-
                    <lb/>
                  fius circuli, ex eodem Archimede. </s>
                  <s xml:id="echoid-s3313" xml:space="preserve">Et ſic cognoſcemus quartam partem ſuperficiei
                    <lb/>
                  ſphæricæ ſphærę propoſite ex .31. primi lib. de ſphæra, & cyllindro Archimedis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3314" xml:space="preserve">Deinde ſumatur tertia pars producti, quod fit ex ſemidiametro in ſuperficiem
                    <lb/>
                  maioris circuli, & habebimus conum, cuius baſis erit circulus maior, altitudo verò
                    <lb/>
                  ſemidiameter propoſitæ ſphæræ ex .9. duodecimi Eucli.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3315" xml:space="preserve">Quadruplum poſtea huiuſmodi coni, erit quantitas ſoliditatis, ſeu corporeitas to
                    <lb/>
                  tius ſphærę ex .32. dicti lib. Archimedis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3316" xml:space="preserve">Imaginemur poſtea
                    <reg norm="in" type="wordlist">ĩ</reg>
                  ſphærica portione
                    <var>.n.e.u.</var>
                    <reg norm="lineam" type="context">lineã</reg>
                    <var>.e.u.</var>
                  à
                    <reg norm="summitate" type="context">sũmitate</reg>
                  ad
                    <reg norm="extremitatem" type="context">extremitatẽ</reg>
                    <lb/>
                  baſis, cuius
                    <var>.e.u.</var>
                  quantitatem cognoſcemus, hoc modo ſcilicet, fumendo
                    <reg norm="radicem" type="context">radicẽ</reg>
                  qua-
                    <lb/>
                  dratam producti
                    <var>.c.e.</var>
                  in
                    <var>.e.a.</var>
                  eo quod
                    <lb/>
                  quadratum
                    <var>.e.u.</var>
                  æquale eſt quadrato
                    <lb/>
                    <figure xlink:label="fig-0277-01" xlink:href="fig-0277-01a" number="308">
                      <image file="0277-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0277-01"/>
                    </figure>
                    <var>a.u.</var>
                  & quadrato
                    <var>.a.e.</var>
                  ex penultima
                    <lb/>
                  primi Eucli. </s>
                  <s xml:id="echoid-s3317" xml:space="preserve">hoc eſt producto quod
                    <lb/>
                  fit ex
                    <var>.c.a.</var>
                  in
                    <var>.a.e.</var>
                  ex .34. tertij
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                  ,
                    <lb/>
                  & quadrato
                    <var>.a.e.</var>
                  hoc eſt producto,
                    <lb/>
                  quod fit ex
                    <var>.c.e.</var>
                  in
                    <var>.e.a.</var>
                  ex .3. ſecundi
                    <lb/>
                  eiuſdem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3318" xml:space="preserve">Inuenta poſtea
                    <var>.e.u.</var>
                  ponamus eam
                    <lb/>
                  vnius circuli ſemidiametrum eſſe, cu
                    <lb/>
                  ius ſuperficialis quantitas etiam inue
                    <lb/>
                  niatur, vt ſupra dictum eſt, quæ qui
                    <lb/>
                    <reg norm="dem" type="context">dẽ</reg>
                  æqualis erit ſuperficiei portionis
                    <lb/>
                    <var>n.e.u.</var>
                  ex .40. primi li. </s>
                  <s xml:id="echoid-s3319" xml:space="preserve">Archimedis de
                    <lb/>
                  ſphæra, & cyllindro.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3320" xml:space="preserve">Hæc autem quantitas vltimo
                    <reg norm="inuem" type="context">inuẽ</reg>
                    <lb/>
                  ta multiplicetur cum tertia parte ſe-
                    <lb/>
                  midiametri datæ ſphæræ, & habebi-
                    <lb/>
                  mus ſoliditatem vnius coni æqualis
                    <lb/>
                  aggregato ſoliditatis portionis
                    <var>.n.e.
                      <lb/>
                    u.</var>
                  ſimul ſumptę
                    <unsure/>
                  ,
                    <reg norm="cum" type="context">cũ</reg>
                  ſoliditate vnius co
                    <lb/>
                  ni, cuius axis ſit
                    <var>.a.o.</var>
                    <reg norm="reſiduum" type="context">reſiduũ</reg>
                  ſemidia-
                    <lb/>
                  metri noſtræ ſphæræ dempta
                    <var>.a.e.</var>
                  ba­ </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum